Find the name and serial number of the unit. The working part is usually the motorized or solenoid head on the tank. If the tanks are in good condition, then the head can be replaced if you can find a source. The manufacturer on the plate would be able to tell you which plumbing supplier can order it.
If the part is no longer available or determinable, the plumber can be right about having to replace the entire unit. here may also be a benefit in getting an improved new model.